Matematika

Pertanyaan

1. jika fungsi f (x) = 4x+5 dengan g(x) = 2x-3 / 4x+7 maka nilai dari (gof)-1 (1) adalah...
2. jika f (x) = 5x+2 dan (fog) 0 =32 - 20x. maka boleh dari g-1 (x) adalah?
tolong bgt yg pinter jawabin smg yg bntu masuk syurganya Allah amiin.

2 Jawaban

  • 1.f-1(x) = x-5/4
       f-1(1) =1-5/4
       f-1(1) = -1
       g(-1) = 2(-1)-3/4(-1)+7
       g(-1) = -5/-11
                = 5/11 
       maaf kalau salah 

  • Fungsi invers

    1.
    f(x) = 4x + 5
    g(x)= (2x-3)/(4x+7)

    gof(x)= g { f(x)} = [ 2(4x+5) - 3  ] / [ 4(4x+5) + 7 ]
    gof(x) = [ 8x+10-3 ] / [ 16x+20+7 ]
    gof(x)= (8x +7)/ (16x + 27)
    .
    (gof)⁻¹ {(8x+7)/(16x+27) = x
    (gof)⁻¹ (1) = ...

    (8x + 7) /(16x + 27) = 1
    1(16x + 27) = 8x + 7
    16x  + 27 = 8x + 7
    16x -8x = 7 - 27
    8x = -20
    x = -20/8
    x = - 5/4

    2.
    f(x)=5x+2

    fog(x) = 32 - 20x
    f {g(x)} = 32 - 20x
    5. g(x) +2 = 32 - 20x
    5. g(x)= -20x + 32 -2
    5. g(x)= -20x + 30
    g(x)= -4x + 6
    y = -4x + 6
    4x = 6-y
    x = 1/4 (6 -y)
    g⁻¹(x)= 1/4 (6 - x)

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